Showing papers by "Manfried Faber published in 1999"
TL;DR: In this article, the structure of center vortices in maximal center gauge of SU(2) lattice gauge theory at zero and finite temperature was investigated and the Euler characteristic of these surfaces was determined.
Abstract: We investigate the structure of center vortices in maximal center gauge of SU(2) lattice gauge theory at zero and finite temperature. In center projection the vortices (called P-vortices) form connected two dimensional surfaces on the dual four-dimensional lattice. At zero temperature we find, in agreement with the area law behaviour of Wilson loops, that most of the P-vortex plaquettes are parts of a single huge vortex. Small P-vortices, and short-range fluctuations of the large vortex surface, do not contribute to the string tension. All of the huge vortices detected in several thousand field configurations turn out to be unorientable. We determine the Euler characteristic of these surfaces and find that they have a very irregular structure with many handles. At finite temperature P-vortices exist also in the deconfined phase. They form cylindric objects which extend in time direction. After removal of unimportant short range fluctuations they consist only of space-space plaquettes, which is in accordance with the perimeter law behaviour of timelike Wilson loops, and the area law behaviour of spatial Wilson loops in this phase.
35 citations
TL;DR: In this paper, the structure of center vortices in maximal center gauge of SU(2) lattice gauge theory at zero and finite temperature was investigated and the Euler characteristic of these surfaces was determined.
Abstract: We investigate the structure of center vortices in maximal center gauge of SU(2) lattice gauge theory at zero and finite temperature. In center projection the vortices (called P-vortices) form connected two dimensional surfaces on the dual four-dimensional lattice. At zero temperature we find, in agreement with the area law behaviour of Wilson loops, that most of the P-vortex plaquettes are parts of a single huge vortex. Small P-vortices, and short-range fluctuations of the large vortex surface, do not contribute to the string tension. All of the huge vortices detected in several thousand field configurations turn out to be unorientable. We determine the Euler characteristic of these surfaces and find that they have a very irregular structure with many handles. At finite temperature P-vortices exist also in the deconfined phase. They form cylindric objects which extend in time direction. After removal of unimportant short range fluctuations they consist only of space-space plaquettes, which is in accordance with the perimeter law behaviour of timelike Wilson loops, and the area law behaviour of spatial Wilson loops in this phase.
35 citations
TL;DR: In this article, the authors introduce a model designed to describe charged particles as stable topological solitons of a field with values on the internal space S^3, which behaves like particles with relativistic properties like Lorentz contraction and velocity dependence of mass.
Abstract: We introduce a model designed to describe charged particles as stable topological solitons of a field with values on the internal space S^3. These solitons behave like particles with relativistic properties like Lorentz contraction and velocity dependence of mass. This mass is defined by the energy of the soliton. In this sense this model is a generalisation of the sine-Gordon model from 1+1 dimensions to 3+1 dimensions, from S^1 to S^3. (We do not chase the aim to give a four-dimensional generalisation of Coleman's isomorphism between the Sine-Gordon model and the Thirring model which was shown in 2-dimensional space-time.) For large distances from the center of solitons this model tends to a dual U(1)-theory with freely propagating electromagnetic waves. Already at the classical level it describes important effects, which usually have to be explained by quantum field theory, like particle-antiparticle annihilation and the running of the coupling.
22 citations
TL;DR: In this paper, the authors argue that the vortex-finding property of maximal center gauge is the key to its success in extracting the vortex content of thermalized lattice configurations and explain how this property comes about, and why it is expected not only in maximal center-gauges, but also in an infinite class of gauge conditions based on adjoint-representation link variables.
Abstract: We argue that the ``vortex-finding'' property of maximal center gauge, i.e. the ability of this gauge to locate center vortices inserted by hand on any given lattice, is the key to its success in extracting the vortex content of thermalized lattice configurations. We explain how this property comes about, and why it is expected not only in maximal center gauge, but also in an infinite class of gauge conditions based on adjoint-representation link variables. In principle, the vortex-finding property can be foiled by Gribov copies. This fact is relevant to a gauge-fixing procedure devised by Kovacs and Tomboulis, where we show that the loss of center dominance, found in their procedure, is explained by a corresponding loss of the vortex-finding property. The association of center dominance with the vortex-finding property is demonstrated numerically in a number of other gauges.
19 citations
TL;DR: In this article, the authors consider projections of SU(2) lattice link variables onto Z2 center and U(1) subgroups, with and without gauge-fixing.
Abstract: We consider projections of SU(2) lattice link variables onto Z2 center and U(1) subgroups, with and without gauge-fixing. It is shown that in the absence of gauge-fixing, and up to an additive constant, the static quark potential extracted from projected variables agrees exactly with the static quark potential taken from the full link variables; this is an extension of recent arguments by Ambjorn and Greensite, and by Ogilvie. Abelian and center dominance is essentially trivial in this case, and seems of no physical relevance. The situation changes drastically upon gauge fixing. In the case of center projection, there are a series of tests one can carry out, to check if vortices identified in the projected configurations are physical objects. All these criteria are satisfied in maximal center gauge, and we show here that they all fail in the absence of gauge fixing. The non-triviality of center projection is due entirely to the maximal center gauge-fixing, which pumps information about the location of extended physical objects into local Z2 observables.
17 citations
TL;DR: In this paper, the authors argue that the vortex-finding property of maximal center gauge is the key to its success in extracting the vortex content of thermalized lattice configurations and explain how this property comes about, and why it is expected not only in maximal center-gauges, but also in an infinite class of gauge conditions based on adjoint-representation link variables.
Abstract: We argue that the ``vortex-finding'' property of maximal center gauge, i.e. the ability of this gauge to locate center vortices inserted by hand on any given lattice, is the key to its success in extracting the vortex content of thermalized lattice configurations. We explain how this property comes about, and why it is expected not only in maximal center gauge, but also in an infinite class of gauge conditions based on adjoint-representation link variables. In principle, the vortex-finding property can be foiled by Gribov copies. This fact is relevant to a gauge-fixing procedure devised by Kovacs and Tomboulis, where we show that the loss of center dominance, found in their procedure, is explained by a corresponding loss of the vortex-finding property. The association of center dominance with the vortex-finding property is demonstrated numerically in a number of other gauges.
16 citations
01 Oct 1999
TL;DR: In this article, the authors argue that the vortex-finding property of maximal center gauge, i.e., the ability of this gauge to locate center vortices inserted by hand on any given lattice, is the key to its success in extracting the vortex content of thermalized lattice configurations.
Abstract: The authors argue that the vortex-finding property of maximal center gauge, i.e. the ability of this gauge to locate center vortices inserted by hand on any given lattice, is the key to its success in extracting the vortex content of thermalized lattice configurations. The authors explain how this property comes about, and why it is expected not only in maximal center gauge, but also in an infinite class of gauge conditions based on adjoint-representation link variables. In principle, the vortex-finding property can be foiled by Gribov copies. This fact is relevant to a gauge-fixing procedure devised by Kovacs and Tomboulis, where they show that the loss of center dominance, found in their procedure, is explained by a corresponding loss of the vortex-finding property. The dependence of center dominance on the vortex-finding property is demonstrated numerically in a number of other gauges.
13 citations
01 Mar 1999
TL;DR: In this article, the center vortex theory of confinement has been studied in Monte Carlo simulations and an explanation of Casimir scaling and the adjoint string tension was given in terms of center vortex mechanism.
Abstract: We report on two recent developments in the center vortex theory of confinement: (i) the asymptotic scaling of the vortex density, as measured in Monte Carlo simulations; and (ii) an explanation of Casimir scaling and the adjoint string tension, in terms of the center vortex mechanism.
5 citations
TL;DR: In this paper, the dominance of center degrees of freedom is observed in SU(3) lattice gauge theory in maximal center gauge and the full asymptotic string tension is reproduced, after center projection, by the center elements alone.
Abstract: The dominance of center degrees of freedom is observed in SU(3) lattice gauge theory in maximal center gauge. The full asymptotic string tension is reproduced, after center projection, by the center elements alone. When center vortices are removed from lattice configurations, the string tension tends to zero. This provides further evidence for the role played by center vortices in the mechanism of color confinement in quantum chromodynamics, but more extensive simulations with a better gauge-fixing procedure are still needed.
3 citations
Posted Content•
TL;DR: In this paper, the relativistic field theory model of the deuteron (RFMD) was used to calculate the astrophysical factor for the solar proton burning, p + p -> D + positron + neutrino.
Abstract: The astrophysical factor S_pp(0) for the solar proton burning, p + p -> D + positron + neutrino, is recalculated in the relativistic field theory model of the deuteron (RFMD). We obtain S_pp(0) = 4.08 x 10^{-25} MeV b which agrees good with the recommended value S_pp(0) = 4.00 x 10^{-25} MeV b. The amplitude of low-energy elastic proton-proton (pp) scattering in the singlet S-wave state with the Coulomb repulsion contributing to the amplitude of the solar proton burning is described in terms of the S-wave scattering length and the effective range. This takes away the problem pointed out by Bahcall and Kamionkowski (Nucl. Phys. A625 (1997) 893) that in the RFMD one cannot describe low-energy elastic pp scattering with the Coulomb repulsion in agreement with low-energy nuclear phenomenology. The cross section for the neutrino disintegration of the deuteron, neutrino + D -> electron + p + p, is calculated with respect to S_pp(0) for neutrino energies from threshold to 10 MeV. The results can be used for the analysis of the data which will be obtained in the experiments planned by SNO. The astrophysical factor S_pep(0) for the pep process, p + electron + p -> neutrino + D, is calculated relative to S_pp(0) in complete agreement with the result obtained by Bahcall and May (ApJ. 155 (1969) 501).
3 citations
Posted Content•
TL;DR: In this article, the relativistic field theory model of the deuteron (RFMD) was evaluated by taking into account the contributions of chiral one-meson loop corrections and the Delta(1232) resonance.
Abstract: The cross sections for the M1-capture n + p -> D + gamma, the photo-magnetic and anti-neutrino disintegration of the deuteron are evaluated in the relativistic field theory model of the deuteron (RFMD) The cross section for M1-capture is evaluated by taking into account the contributions of chiral one-meson loop corrections and the Delta(1232) resonance The cross sections for the photo-magnetic and anti-neutrino disintegration of the deuteron are evaluated by accounting for final-state interaction of the nucleon pair in the spinsinglet S-wave state The amplitudes of low-energy elastic np and nn scattering contributing to these processes are obtained in terms of the S-wave scattering lengths and the effective ranges This relaxes substantially the statement by Bahcall and Kamionkowski (Nucl Phys A625 (1997) 893) that the RFMD is unable to describe a non-zero effective range for low-energy elastic nucleon-nucleon scattering The cross sections for the anti-neutrino disintegration of the deuteron averaged over the anti-neutrino energy spectrum agree good with experimental data
Posted Content•
TL;DR: The relativistic field theory model of the deuteron (RFMD) is formulated from the first principles of QCD in this paper, and it is shown that contributions of nucleon-loop anomalies to effective Lagrangians of low-energy nu- clear interactions are justified in the large NC expansion, where NC is the number of quark colours.
Abstract: The relativistic field theory model of the deuteron (RFMD) is re- formulated from the first principles of QCD. The deuteron appears as a neutron-proton collective excitation, i.e. a Cooper np-pair, induced by a phenomenological local four-nucleon interaction in the nuclear phase of QCD. The RFMD describes the deuteron coupled to hadrons through one-nucleon loop exchanges providing a minimal transfer of nucleon flavours from initial to final nuclear states and accounting for contributions of nucleon-loop anomalies which are completely deter- mined by one-nucleon loop diagrams. The dominance of contributions of nucleon-loop anomalies to effective Lagrangians of low-energy nu- clear interactions is justified in the large NC expansion, where NC is the number of quark colours.
TL;DR: In this article, the magnetic monopole condensate was calculated in the dual Monopole Nambu-Jona-Lasinio model with dual Dirac strings.
Abstract: The magnetic monopole condensate is calculated in the dual Monopole Nambu–Jona–Lasinio model with dual Dirac strings suggested in [1,2] as a functional of the dual Dirac string shape. The calculation is carried out in the tree approximation in the scalar monopole–antimonopole collective excitation field. The integration over quantum fluctuations of the dual–vector monopole–antimonopole collective excitation field around the Abrikosov flux line and string shape fluctuations are performed explicitly. We claim that there are important contributions of quantum and string shape fluctuations to the magnetic monopole condensate.
Posted Content•
TL;DR: In this paper, the authors address two questions related to the procedure of identifying center vortices based on center projection in maximal center gauge: 1) How does the procedure work, why is it expected to locate center Vortices relevant for confinement, and why does it in some cases fail, on lattice configurations preconditioned in a special way.
Abstract: We address two questions related to the procedure of identifying center vortices based on center projection in maximal center gauge: 1. How does the procedure work, why is it expected to locate center vortices relevant for confinement, and why does it in some cases fail, on lattice configurations preconditioned in a special way? 2. Does the mechanism work the same way for 3 colors instead of 2? (The paper is an abridged version of two recent e-prints, hep-lat/9910033 and hep-lat/9911006.)
TL;DR: In this article, the authors considered the dual monopole Nambu-Jona-Lasinio model with dual Dirac string length and showed that the dominant role of quantum fluctuations for the formation of the linearly rising part of the confinement potential is argued.
Abstract: Interquark confinement potential is calculated in the dual monopole Nambu–Jona–Lasinio model with dual Dirac strings suggested in [2,3] as a functional of the dual Dirac string length. The calculation is carried out by explicit integration over quantum fluctuations of a dual-vector field (monopole–antimonopole collective excitation) around the Abrikosov flux line and string shape fluctuations. The contribution of the scalar field (monopole–antimonopole collective excitation) exchange is taken into account in the tree approximation because of the London limit regime. The dominant role of quantum fluctuations for the formation of the linearly rising part of the confinement potential is argued.
Posted Content•
TL;DR: In this article, the condensation of a dual-vector field with dual Dirac strings is investigated in the dual Monopole Nambu-Jona-Lasinio model.
Abstract: The condensation of a dual–vector field is investigated in the dual Monopole Nambu– Jona–Lasinio model with dual Dirac strings. The condensate of a dual–vector field is calculated as a functional of a shape of a dual Dirac string. The obtained result is compared with the gluon condensate calculated in a QCD sum rules approach and on lattice.
TL;DR: In this article, the structure of center projected vortices of SU(2) lattice gauge theory at zero and finite temperature was investigated and it was shown that most of the P-vortex plaquettes are parts of a single huge vortex.
Abstract: We investigate the structure of center projected vortices of SU(2) lattice gauge theory at zero and finite temperature. At zero temperature we find, in agreement with the area law behaviour of Wilson loops, that most of the P-vortex plaquettes are parts of a single huge vortex. This vortex is an unorientable surface and has a very irregular structure with many handles. Small P-vortices, and short-range fluctuations of the large vortex surface, do not contribute to the string tension. At finite temperature P-vortices exist also in the deconfined phase. However, they form cylindric objects which extend in time direction and consist only of space-space plaquettes.
Posted Content•
TL;DR: The Delta-Delta component of the deuteron, where Delta stands for the Delta(1232) resonance, is calculated in the relativistic field theory model of thedeuteron and the prediction agrees good with the experimental estimate P(Delta-Delta) < 0.4 % at 90 % of CL.
Abstract: The Delta-Delta component of the deuteron, where Delta stands for the Delta(1232) resonance, is calculated in the relativistic field theory model of the deuteron For the probability of the Delta-Delta component of the deuteron we give P(Delta-Delta) = 008 % This prediction agrees good with the experimental estimate P(Delta-Delta) < 04 % at 90 % of CL (D Allasia et al, Phys Lett B174 (1986) 450)